A high-electron-mobility transistor (HEMT) includes a modulation doped heterojunction structure. Because band gaps of two materials composing the heterojunction structure are different, potential wells and potential barriers are formed at the interface of the heterojunction structure after the gate of the heterojunction structure is biased. Because a polarization effect or free electrons are accumulated at the potential wells near the interface of the heterojunction structure, two dimensional electron gases (2-DEG) are formed at the potential wells. Because the two-dimensional electron gas is not affected by scattered impurity ions, the electron mobility of the two dimensional electron gas is very high. Moreover, an impurity center is not frozen at a very low temperature because electrons are spaced apart the impurity center, so that HEMT has a very perfect performance at a very low temperature and can be used for a research work (such as fractional quantum Hall effect) at a very low temperature. HEMT is a voltage controlling device, and the depths of the potential wells can be regulated by the gate voltage (Vg) to control the surface density of 2-DEG in the potential wells to control HEMT's operating current. A middle region of an ingot with the same diameter only can be used for cutting a wafer, and head and tail regions of the ingot need to be removed. Because the weights of the head and tail regions gradually increase with the diameter of the ingot, it needs to recycle the ingot for reducing the cost and enhancing the performance.